Two-dimensional (2D) materials, particularly semiconducting transition metal dichalcogenides (TMDs) like WS₂, are attracting significant interest for their potential in quantum information technologies, precision metrology, and imaging. WS₂ monolayers, with their direct band gap in the visible range, are especially promising. However, their large surface-to-volume ratio makes their optoelectronic properties highly sensitive to the surrounding environment. Exposure to air, and specifically oxygen adsorption, significantly alters WS₂'s conductivity and photoluminescence (PL) emission. While oxygen's electron-withdrawing nature is well-established, a comprehensive atomistic-level explanation of the electron transfer mechanism has been lacking. Existing theoretical analyses often rely on charge population analysis (CPA), neglecting the intrinsic n-doping of WS₂ and the presence of defects. CPA often yields negligible electron fractions, which depend heavily on the chosen partition scheme and are difficult to translate into meaningful changes in carrier concentration. This study addresses these limitations by developing a more robust and physically sound method for characterizing surface charge transfer in 2D materials exposed to gas atmospheres. The aim is to provide a more accurate model for the interaction between oxygen and WS₂, considering both intrinsic properties and the influence of defects.

Numerous studies have explored the effects of oxygen adsorption on WS₂ monolayers, observing a decrease in conductivity and changes in PL spectra. The PL enhancement observed in air compared to vacuum has been attributed to electron withdrawal by adsorbed oxygen molecules, leading to reduced free electron density and favoring the formation of neutral excitons. While chemisorption of oxygen has been considered, it's an energy-activated process with significant impact only at high laser power or prolonged irradiation. Physisorption on the basal plane is generally considered the primary contributor to PL enhancement. Most theoretical works, however, focus on pristine surfaces, overlooking the presence of defects, such as sulfur vacancies (Vs), which are prevalent in synthesized 2D materials and significantly affect their reactivity and catalytic properties. These defects are known to enhance the reactivity towards various chemical species, including oxygen. Therefore, a comprehensive model must account for these defects to accurately describe the oxygen adsorption process.

This research employs ab initio simulations based on Density Functional Theory (DFT) to analyze the electron transfer mechanism in WS₂ monolayers exposed to air. The calculations utilize spin-polarized DFT as implemented in Quantum Espresso, employing norm-conserving pseudopotentials and the rev-vdW-DF2 van der Waals density functional to accurately model dispersion forces. Electronic wavefunctions are expanded in plane waves, and the Brillouin zone is sampled using a Monkhorst-Pack mesh. Large supercells (5x5 to 7x7 unit cells) were used to model sulfur vacancies and adsorbed molecules (O₂ and N₂). The intrinsic n-type character of WS₂ was simulated by explicitly adding extra electrons to the supercells. The adsorption energy of molecules on pristine surfaces and sulfur vacancies was calculated, accounting for energy correction terms to address the effects of charged supercells. The Gibbs free energy of formation for various configurations (neutral and charged sulfur vacancies, with and without adsorbed molecules) was determined as a function of the Fermi level. The charge transition levels were then calculated to determine the stability of each configuration. The fraction of vacancy sites occupied by each species in different charge states was calculated using a Boltzmann distribution. To simulate n-doped samples, a free electron density source term was introduced into the charge balance equation, alongside the sulfur vacancy concentration. This allowed the calculation of the equilibrium Fermi level and free electron density in different environments (vacuum, N₂ atmosphere, and air). The relative enhancement of the neutral exciton peak (X⁰) compared to the negative trion peak (X⁻) in the PL spectrum was calculated and related to the free electron density and Fermi level. Finally, the electronic properties, band diagrams, and partial densities of states (PDOS) were analyzed to clarify the electron transfer mechanism. Charge population analysis (CPA) was also performed for comparison, highlighting its limitations.

The study's key findings demonstrate that the adsorption of O₂ on the pristine surface of WS₂ monolayers does not induce electron transfer. However, the presence of sulfur vacancies (Vs) dramatically changes this. Oxygen physisorption on Vs sites, in conjunction with the material's intrinsic n-type nature, facilitates a charge transfer from the WS₂ conduction band to localized surface states introduced by the adsorbed oxygen. This leads to a decrease in the free electron concentration and a corresponding increase in the neutral exciton peak (X⁰) relative to the negative trion peak (X⁻) in PL measurements. The magnitude of the reduction in free electron density and the PL enhancement depends on the density of sulfur vacancies and the level of n-doping. In contrast, nitrogen (N₂), an inert molecule, shows no significant impact on the WS₂ electron density, validating the selectivity of the observed effect for oxygen. Analysis of the band diagrams and PDOS provides further evidence of electron transfer to the oxygen molecule adsorbed on sulfur vacancies, with the additional electron occupying a state with significant contribution from oxygen p₂ orbitals. The method used here overcomes the shortcomings of conventional CPA, which often fails to accurately quantify the electron transfer and its impact on optoelectronic properties due to its dependence on arbitrary charge partitioning schemes and inability to easily incorporate parameters such as defect density and n-type doping. The method employed here successfully distinguishes between active (O₂) and inert (N₂) molecules, demonstrating its effectiveness.

The results significantly advance our understanding of the interaction between gas molecules and 2D materials. The proposed method, explicitly accounting for the intrinsic properties and defect landscape of WS₂, accurately describes the modulation of free electron concentration upon oxygen adsorption. The observed PL enhancement, consistent with experimental observations, is directly linked to the electron transfer facilitated by the presence of sulfur vacancies. The study's success in differentiating the behavior of reactive and inert molecules further validates the method's accuracy and general applicability. The findings highlight the critical role of defects in determining the response of 2D materials to their environment, providing crucial insights for designing and optimizing devices based on these materials.

This work elucidates the mechanism behind the alteration of WS₂ monolayer optoelectronic properties upon exposure to air. The novel approach, which goes beyond traditional CPA, provides a robust and accurate means of evaluating charge transfer upon molecular adsorption. The crucial roles of sulfur vacancies and intrinsic n-type doping in mediating this electron transfer were identified. Future research could extend this methodology to other 2D materials and different gas molecules, exploring the broader applicability and further refining the model's predictive power. Investigating the effects of different defect types and concentrations would also enhance our understanding of the interplay between defects and gas adsorption in influencing the material's properties.

While the model effectively captures the key aspects of oxygen physisorption and electron transfer in n-doped WS₂ monolayers, several factors could be considered for future refinement. The model assumes a uniform distribution of sulfur vacancies and a constant level of n-doping, which may not precisely reflect the complexity of real samples. More detailed analysis of the effects of specific defect arrangements, inhomogeneities in defect density, and other potential dopants could provide more nuanced insights. Furthermore, interactions with the substrate, if present, were not directly accounted for in the model.